Energy and non energy Commodities: Spillover Effects on ...

Journal of Statistical and Econometric Methods, Vol. 9, No. 4, 2020, 91-115

ISSN: 2241-0384 (print), 2241-0376 (online)

https://doi.org/10.47260/jsem/vol947 Scientific Press International Limited

Energy and non–energy Commodities: Spillover

Effects on African Stock Markets

Alessandra Amendola1, Marinella Boccia2, Vincenzo Candila3

and Giampiero M. Gallo4

Abstract

This paper examines the volatility transmission from energy and metal commodities

to six major African exporters’ stock markets (Egypt for oil and gold, Nigeria for

oil and gas, South Africa for coal and gold, Tunisia for oil, Uganda for gold and

Zambia for copper). Modelling commodity volatility with the Double Asymmetric

GARCH-MIDAS model with a Student’s t-distribution allows to detect the presence

of impact and inertial stock market volatility spillovers at different lags and to take

into account the leptokurtosis of the commodity series. We then derive the profile

of Volatility Impulse Responses of the stock markets to commodity shocks.

JEL classification numbers: C10, C52, C58.

Keywords: Volatility spillover, GARCH-MIDAS, African countries, Commodities.

1 Dept. of Economics and Statistics, University of Salerno, Italy. 2 Dept. of Economics and Statistics, University of Salerno, Italy. 3 MEMOTEF Department, Sapienza University of Rome, Italy. 4 Italian Court of Audits (Corte dei conti), and NYU in Florence, Italy.

Article Info: Received: August 14, 2020. Revised: August 25, 2020.

Published online: August 27, 2020.

https://doi.org/10.47260/jsem/vol947

92 Amendola et al.

1. Introduction

Investigating interdependencies across asset classes allows to exploit the benefits of

portfolio diversification: in the case of commodity prices and stock markets we have

an additional interest also because several economies are dependent on commodity

trading, and movements in commodity prices are an important cost component of

manufactured goods through energy and raw materials (Silvennoinen and Thorp,

2013). Several contributions focus on the interconnections of advanced economies

between commodities (for instance, Karanasos et al., 2018 and Nazlioglu et al.,

2013), stock markets (Hou and Li, 2020 and Berg and Vu, 2019), currencies

(Greenwood-Nimmo et al., 2016) and all their possible interactions (Ildırar and

Iscan, 2016 and Kang et al., 2015, among others). More recent is the interest about

the volatility spillovers among the stock markets of emerging countries and/or

among these latter and developed countries. For instance, Engle et al. (2012)

analyze volatility spillovers in East Asia surrounding the 1997 crisis, Korkmaz et

al. (2012) the return and volatility spillovers among six emerging countries

(Colombia, Indonesia, Vietnam, Egypt, Turkey, and South Africa). Kim et al. (2015)

and Neaime (2012) investigate the impact of the 2007 financial crisis on five

emerging Asian economies and on the Middle East and North Africa stock markets,

respectively. However, to the best of our knowledge, the issue of how strong

reliance of African emerging economies on commodity exports, whose price

volatility may influence these stock markets, has not received adequate attention.

In this paper we examine the volatility spillovers between four energy and metal

commodities (Oil, Gas, Gold and Copper) chosen among the top exporting goods

of six African countries (Egypt, Nigeria, South Africa, Tunisia, Uganda, Zambia)

and the stock markets of these countries. In particular, Egypt, Nigeria and Tunisia

mainly export Oil, South Africa has a relevant share of Gas exports, Uganda

primarily Gold and Zambia mostly exports Copper.

From an economic viewpoint, our interest is also motivated by the consequences

produced on these countries by the increasing trend in commodity prices registered

at the beginning of 2000s: a contribution to the development of these export-based

economies and a larger foreign investor inflow towards these stock markets (Adjasi

and Yartey, 2007). According to the statistics reported in the 2018 African yearbook

(Economic Commission for Africa et al., 2018), the African countries here

considered in 2018 represent almost one half of the overall African GDP. By the

same token, the exchanges considered represent approximately 93% of the total

African market capitalization (in 2017) even if they are of limited importance at the

world level. In fact, they have no feedback on the global markets fixing the price of

these commodities, so it is natural to focus on the unilateral spillovers from a

commodity market volatility to a stock exchange. At the same time, there is little, if

any, interdependence across markets, so we will not examine spillovers from one

country to another.

The literature on volatility spillovers is sizeable and dates back to the early works

of Hamao et al. (1990), Engle et al. (1990), and Lin et al. (1994) in an effort to

Energy and non–energy Commodities: Spillover Effects on African Stock Markets

93

extend the univariate GARCH (Bollerslev, 1986) model. So far, different

approaches to estimating volatility spillovers have been proposed. For instance,

Diebold and Yilmalz (2009, 2012) consider forecast-error variance decomposition

within a vector autoregression as a tool through which a spillover index can be

calculated. Another approach falls within the multivariate generalized

autoregressive conditional heteroskedasticity [MGARCH] (Bauwens et al., 2006)

model. Typically a BEKK (Engle and Kroner, 1995) specification is used to

estimate the conditional covariance matrices of the involved markets. Subsequently,

the volatility impulse response function [VIRF] methodology proposed by Hafner

and Herwartz (2006) is employed. The VIRF investigates the impact (in terms of

size and persistence) of shocks originating in the source of volatility spillover and

hitting the (expected) conditional volatility of the recipient. Recently, the

MGARCH-VIRF methodology has been applied in different contributions (for

instance, Candila and Farace, 2018 and Kang et al., 2017). Rather than relying on

estimated conditional variances (and covariances) starting from daily returns, the

method suggested by Engle et al. (2012) directly considers the conditional

expectations of the daily range, in a Multiplicative Error Model [MEM] context

(Engle, 2002 and Engle and Gallo, 2012) in order to identify volatility spillovers

and VIRF.

Our analysis rests on a methodological approach conceptually divided in three steps.

In the first step, the absence/presence of volatility spillover from a source (a

commodity) to a recipient (an African stock market index) is tested. In the second

step, a bivariate BEKK-MGARCH model is estimated for the relationships source–

recipient signalled by the test. In the last step, the VIRF is derived to verify the size

and the impact of a shock from the origin to the recipient.

As regards the first step, the absence of shock and volatility relationships can be

easily tested through the approach proposed by Chang and McAleer (2017). In the

original formulation, the test aims at verifying whether the squared returns (impact)

and the estimated volatility (inertia) of another market (origin) has explanatory

power for the volatility of the recipient. Chang and McAleer (2017) suggest to

estimate both these volatilities by considering an extended univariate GARCH

specification. This notwithstanding, commodities demand is related to the business

cycle and hence its price movements are influenced by some macroeconomic

variables [MVs] (e.g. the US Industrial Production index [IndPro], the exchanged

volume of commodities, the real exchange rate, the GDP growth, and so forth, as

suggested by Chevallier and Ielpo (2013), Bapna et al. (2012), and Borensztein and

Reinhart (1994), among others). A problem arising in this context is the discrepancy

between the frequency at which the stock market index is observed (i.e., daily) and

the frequency of the MV observations (usually, monthly or quarterly). A solution

could be to lower the daily frequency of the stock market index to harmonize it with

the MV of interest, as done by Diebold and Yilmaz, 2008, for instance. Another and

more recent solution is to mix both the frequencies, by the so-called GARCH-

MIDAS (Engle et al., 2013) approach. Recent contributions on this latter approach

can be found in Mo et al. (2018), Amendola et al. (2017), and Conrad and Lock

94 Amendola et al.

(2015), in the univariate framework and in Asgharian et al. (2015) and Conrad et al.

(2014) in the multivariate context. The possible different impact had by positive and

negative MV variations on the dependent variable is inserted in Amendola et al.

(2019), where the filter of the MVs consists of separating the positive and negative

MV realizations. In view of its successful contribution in explaining volatility, we

take their Double-Asymmetric GARCH-MIDAS [ DAGM ] model to be

implemented in the testing framework of Chang and McAleer (2017). Another

contribution of the present paper is that we estimate the DAGM model in a Student’s

t context, in order to successfully take into account the heavy tails of the commodity

returns under investigation. The test employed here highlights that the impact and

inertia of Oil influence the stock markets volatility of Egypt, Nigeria, Tunisia and

Zambia, Gold that of Uganda and Zambia and Copper affects the volatility of

Tunisia, Uganda and Zambia stock markets. Interestingly, among these

relationships emerged by the test, some have also an economic interpretation. In

fact, the energy and metal commodities having the largest share of exports in Egypt

(Oil), Nigeria (Oil), Tunisia (Oil), Uganda (Gold) and Zambia (Copper) are the

same commodities influencing these stock markets. Instead, the stock market of

South Africa seems to be unaffected by the impact and inertia originating from the

commodities considered. This is in line with the findings of Sugimoto et al., 2014,

where, even though the attention is more on impact spillovers, the authors claim

that Gold and Oil commodities modestly affect African stock markets.

After having estimated the BEKK specification for each of the previous ten

relationships, the VIRF is used as a tool to describe the response of the stock market

index to shocks occurring in the commodity markets. The analysis in this step is

restricted to the relationships where all the estimated coefficients are found

significant. The most relevant effects take place after negative daily returns for

Copper, when the volatility of Uganda and Zambia increases up to 2% the day after

the shock, while the persistence of these volatility shocks vanishes after

approximately 50 days.

The rest of the paper is organized as follows. Section 2 presents the three-step

analysis. Section 3 details the results. Conclusions follow.

2. Methodology

Throughout the paper, the series 𝑖 and 𝑗 indicate respectively the receiver and the

origin of the volatility spillover. Moreover, we adopt the expression “𝑗 → 𝑖” to

denote the occurrence of a volatility spillover from 𝑗 to 𝑖. Adopting a standard

notation, 𝑦𝑣,𝑡 represents the log-returns (close-to-close) of the series 𝑣 at time 𝑡,

usually a day, that is: 𝑦𝑣,𝑡 = log(𝑃𝑣,𝑡) − log(𝑃𝑣,𝑡−1). Furthermore, we assume that:

𝑦𝑣,𝑡 = 𝐸(𝑦𝑣,𝑡|𝐼𝑡−1) + 𝜖𝑣,𝑡, with 𝑣 = 𝑖, 𝑗, (1)


95

where 𝐸(𝑦𝑣,𝑡|𝐼𝑡−1) represents the expected return conditional on the information

set 𝐼𝑡−1, and 𝜖𝑣,𝑡 is the heteroskedastic error term, such that

𝜖𝑣,𝑡 = ℎ𝑣,𝑡𝑧𝑡, (2)

where 𝑧𝑡 is a random sequence of i.i.d. distributed variables with mean zero and

unit variance and ℎ𝑣,𝑡 is the conditional standard deviation for series 𝑣 . The

GARCH specification to model the conditional variance ℎ𝑣,𝑡2 for the series 𝑣 is:

ℎ𝑣,𝑡2 = 𝑤𝑣 + 𝛼𝑣𝜖𝑣,𝑡−1

2 + 𝛽𝑣ℎ𝑣,𝑡−12 , (3)

where 𝑤𝑣 is the constant and 𝛼𝑣 and 𝛽𝑣 are the so-called ARCH and GARCH

parameters, respectively. In order to test the volatility spillover from commodity 𝑗

(origin) to series 𝑖 (recipient), Chang and McAleer (2017) proposed to add lagged

squared returns and variances of series 𝑗 to Eq. (3), which, when series 𝑖 and 𝑗

are simultaneously included, becomes:

ℎ𝑖,𝑡2 = 𝑤𝑖 + 𝛼𝑖𝜖𝑖,𝑡−1

2 + 𝛽𝑖ℎ𝑖,𝑡−12 + 𝛼𝑗𝜖𝑗,𝑡−1

2 + 𝛽𝑗ℎ𝑗,𝑡−12 . (4)

In this formulation, 𝛼𝑗 represents the effect of a shock or impact spillover from

series 𝑗 to series 𝑖 , while 𝛽𝑗 represents the effect of a volatility or inertial

spillover. Some possible extensions, which will not be covered in this paper, include

bidirectional (that is, 𝑗 → 𝑖 and 𝑖 → 𝑗), contemporaneous (𝑗 → 𝑖, with both the

series are at time 𝑡) and non-causal relationships (𝑗 → 𝑖 , with 𝑗 at time 𝑡 + 1

influences 𝑖 at time 𝑡).

The null of no (shock and inertial) volatility spillover, alternatively defined as

Granger non-causality (Granger, 1969), is:

𝐻0: 𝛼𝑗 = 𝛽𝑗 = 0. (5)

The test in (5) can be easily carried out through a Likelihood Ratio [LR] approach,

where the log-likelihood of the unrestricted model (Eq. (4), with parameter space

Θ𝑈𝑁𝑅 = {𝑤𝑖, 𝛼𝑖, 𝛽𝑖, 𝛼𝑗 , 𝛽𝑗}) is compared to that of the restricted one (as expressed

by Eq. (3), with 𝑣 = 𝑖 and Θ𝑅 = {𝑤𝑖, 𝛼𝑖, 𝛽𝑖}).

According to Eq. (4), currently the LR test would only allow for impact and inertial

spillovers originating in series 𝑗 at time 𝑡 − 1 and having some effects on series

𝑖 at time 𝑡 . However, such configuration may lead also to some spurious

interdependencies. The evaluation of volatility spillover existence from 𝑗 to 𝑖 would be much more strengthened if the null was rejected independently of the

lagged periods 𝑡 − 𝑙, with 𝑙 = {1,2,3}, for instance. Hence, we change Eq. (4) to:

ℎ𝑖,𝑡2 = 𝑤𝑖 + 𝛼𝑖𝜖𝑖,𝑡−1

2 + 𝛽𝑖ℎ𝑖,𝑡−12 + 𝛼𝑗𝜖𝑗,𝑡−𝑙

2 + 𝛽𝑗ℎ𝑗,𝑡−𝑙2 , with 𝑙 = {1,2,3}. (6)

96 Amendola et al.

Therefore, the LR test is based on the comparison between the log-likelihoods of

the unrestricted (Eq. (6)) and restricted (Eq. (3)) models.

Finally, we adopt the following definition [Def.] to qualify the existence of a

volatility spillover:

Definition 1 A commodity 𝑗 transfers impact and inertial spillovers to country 𝑖, that is 𝑗 → 𝑖, if and only if the null of the LR test in (5), on the basis of the restricted

model in (3) and the unrestricted model in (6), with 𝑙 = {1,2} , 𝑙 = {2,3} , or

alternatively 𝑙 = {1,2,3}, is rejected at the 1% significance level.

Therefore, the previous definition assumes that 𝑗 → 𝑖 only if at least two LR tests

are rejected at the 1% significance level, with the unrestricted model that includes

(again, at least) two consecutive (lagged) periods for the commodity impact and

inertia.

In this contribution, we estimate the volatility of the commodity 𝑗 taking into

account the fact that some MVs may drive, asymmetrically, its volatility. Then, we

adopt a DAGM expression for ℎ𝑗,𝑡, assuming a multiplicative decomposition of the

conditional variance of the originator, ℎ𝑗,𝑡2 , in Eq. (2), in a short- and long-run

component, such that:

ℎ𝑗,𝑡2 = 𝜏𝑗,𝑚𝑔𝑗,𝑡,𝑚, (7)

where 𝑔𝑗,𝑡,𝑚 indicates the short-run component of the series 𝑗 for day 𝑡 of the

period 𝑚 , and 𝜏𝑗,𝑚 the corresponding long-run component, which in this

configuration varies at a monthly frequency 𝑚, with 𝑚 = 1, ⋯ , 𝑀, given that we

will use monthly observations for the MVs. Furthermore, let 𝐷𝑚 be the number of

days included in month 𝑚 . The total number of daily observations is 𝑇 =∑𝑀

𝑚=1 𝐷𝑚.

The short-run component 𝑔𝑗,𝑡,𝑚 follows a unit mean-reverting GARCH(1,1), that

is:

𝑔𝑗,𝑡,𝑚 = (1 − 𝛼𝑗,𝑠 − 𝛽𝑗,𝑠 − 𝛾𝑗,𝑠/2) + (𝛼𝑗,𝑠 + 𝛾𝑗,𝑠 ⋅ 1(𝜖𝑗,𝑡−1,𝑚<0))(𝜖𝑗,𝑡−1,𝑚)

2

𝜏𝑡+ 𝛽𝑔𝑗,𝑡−1,𝑚, (8)

where the suffix “𝑠” stands for short-run and is used to distinguish the 𝛼 and 𝛽

parameters in Eq. (8) from those in Eq. (6). In addition to 𝛼𝑗,𝑠, we include also 𝛾𝑗,𝑠,

which is the term associated with negative lagged innovation 𝜖𝑗,𝑡−1,𝑚, with 1(.)

being an indicator function that assumes value one if the argument is true. In order

to ensure the positivity of short-run component, the following constraints are set:

𝛼𝑗,𝑠 ≥ 0, 𝛽𝑗,𝑠 ≥ 0 and 𝛼𝑗,𝑠 + 𝛽𝑗,𝑠 + 𝛾𝑗,𝑠/2 < 1.

The long-run component in Eq. (7) is defined as:


97

𝜏𝑗,𝑚 = exp (𝜙𝑗 + 𝜃𝑗+ ∑

𝐾

𝑘=1

𝛿𝑘(𝜔𝑗,2+ )𝑀𝑉𝑚−𝑘1(𝑀𝑉𝑚−𝑘≥0) +

𝜃𝑗− ∑

𝐾

𝑘=1

𝛿𝑘(𝜔𝑗,2− )𝑀𝑉𝑚−𝑘1(𝑀𝑉𝑚−𝑘<0)) (9)

where 𝜃𝑗+ and 𝜃𝑗

− respectively represent the sign–specific parameters associated

with positive and negative 𝐾 lagged MV variations, each of which are weighed

(through 𝛿𝑘(𝜔2+) and 𝛿𝑘(𝜔2

−)) according to a proper weighting function. As in

other works concerning the GARCH-MIDAS, we opt for the Beta function as the

weighting function, which has the following general formulation:

𝛿𝑘(𝜔) =(𝑘/𝐾)𝜔1−1(1−𝑘/𝐾)𝜔2−1

∑𝐾𝑗=1 (𝑗/𝐾)𝜔1−1(1−𝑗/𝐾)𝜔2−1. (10)

with ∑𝐾𝑘=1 𝛿𝑘(𝜔) = 1 and the constraint that 𝜔1 < 𝜔2, which allows for a larger

importance on more recent observations. Moreover, we impose 𝜔1 = 1, in order to

have a monotonically decreasing weighting scheme.

Wanting to consider a greater density in the tails of the conditional distribution of

the commodity series, instead of considering that the log-returns of 𝑗 are

conditionally normally distributed, we assume that they follow a Student’s t-

distribution (Bollerslev, 1987), with 𝑑𝑓 > 2 degrees of freedom, that is:

𝜖𝑗,𝑡,𝑚|𝐼𝑡−1,𝑚 ∼ 𝑓𝑑𝑓(𝜖𝑗,𝑡,𝑚|𝐼𝑡−1,𝑚), (11)

where 𝑓𝑑𝑓 is the (conditional) density function for 𝜖𝑗,𝑡,𝑚, defined as:

𝑓𝑑𝑓(𝜖𝑗,𝑡,𝑚|𝐼𝑡−1,𝑚) = Γ (𝑑𝑓 + 1

2) Γ (

𝑑𝑓

2)

−1

((𝑑𝑓 − 2)ℎ𝑗,𝑡2 )

−1/2

×

(1 +𝜖𝑗,𝑡,𝑚

2

ℎ𝑗,𝑡2 (𝑑𝑓−2)

)−(𝑑𝑓+1)/2

. (12)

The parameters to estimate included in the parameter space of the DAGM plus the

degrees of freedom 𝑑𝑓, Θ𝐷𝐴𝐺𝑀 = {𝛼𝑗,𝑠, 𝛽𝑗,𝑠, 𝛾𝑗,𝑠, 𝜙𝑗 , 𝜃𝑗+, 𝜔𝑗,2

+ , 𝜃𝑗−, 𝜔𝑗,2

− , 𝑑𝑓}, can be

easily obtained maximizing the following log-likelihood:

𝐿(Θ𝐷𝐴𝐺𝑀; 𝑗) = ∑𝑀𝑚=1 {∑𝐷𝑚

𝑡=1 [log (𝑓𝑑𝑓(𝜖𝑗,𝑡,𝑚|𝐼𝑡−1,𝑚))]}. (13)

Now, let us assume that between the series 𝑖 and 𝑗 some volatility spillovers hold

according to Def. 1. In order to further analyse these interdependencies, we adopt

98 Amendola et al.

the VIRF methodology proposed by Hafner and Herwartz (2006), which makes use

of the conditional covariance matrix, labelled as 𝐻𝑡 , derived using the BEKK

model. Let 𝛜𝑡 be a 2 × 1 vector of daily-log returns (if 𝐸(𝑦𝑣,𝑡|𝐼𝑡−1) = 0, for

𝑣 = 𝑖, 𝑗) or residuals, such that:

𝛜𝑡 = 𝐻𝑡1/2

𝐳𝑡, 𝑡 = 1, … , 𝑇, (14)

where the random vector 𝐳𝑡 is assumed to have zero means (𝐸(𝐳𝑡) = 𝟎) and that

𝐸(𝐳𝑡𝐳𝑡′) = 𝐼2, an identity matrix of order 2. Furthermore, 𝐳𝑡 is assumed to follow

a multivariate normal distribution. In the BEKK(1,1) representation, 𝐻𝑡 is

obtained as follows:

𝐻𝑡 = 𝐶𝐶′ + 𝐴𝛜𝑡𝛜𝑡′ 𝐴′ + 𝐺𝐻𝑡−1𝐺′, (15)

with 𝐶 being a lower triangular matrix and 𝐴 and 𝐵 having both dimension

2 × 2. The dynamic structure of a BEKK(1,1) is:

[𝐻𝑖𝑖,𝑡 𝐻𝑖𝑗,𝑡

𝐻𝑗𝑖,𝑡 𝐻𝑗𝑗,𝑡] = [

𝐶𝑖𝑖 0𝐶𝑗𝑖 𝐶𝑗𝑗

] [𝐶𝑖𝑖 𝐶𝑗𝑖

0 𝐶𝑗𝑗] +

[𝐴𝑖𝑖 𝐴𝑖𝑗

𝐴𝑗𝑖 𝐴𝑗𝑗] [

𝜖𝑖𝑖,𝑡−12 𝜖𝑖,𝑡−1𝜖𝑗,𝑡−1

𝜖𝑗,𝑡−1𝜖𝑖,𝑡−1 𝜖𝑗𝑗,𝑡−12 ] [

𝐴𝑖𝑖 𝐴𝑗𝑖

𝐴𝑖𝑗 𝐴𝑗𝑗] +

[𝐺𝑖𝑖 𝐺𝑖𝑗

𝐺𝑗𝑖 𝐺𝑗𝑗] [

𝐻𝑖𝑖,𝑡−1 𝐻𝑖𝑗,𝑡−1

𝐻𝑗𝑖,𝑡−1 𝐻𝑗𝑗,𝑡−1

] [𝐺𝑖𝑖 𝐺𝑗𝑖

𝐺𝑖𝑗 𝐺𝑗𝑗], (16)

with 𝐻𝑖𝑖, 𝐻𝑗𝑗, and 𝐻𝑖𝑗 representing the conditional variances for series 𝑖, 𝑗 and

their conditional covariance at time 𝑡, respectively. The coefficients 𝐴𝑖𝑗 and 𝐴𝑗𝑖

capture the “impact” component of spillovers, while 𝐺𝑖𝑗 and 𝐺𝑗𝑖 apply to the

“inertial” component for lagged covariances. Because of the linkage of interest is

only from series 𝑗 to series 𝑖, we only pay attention to the coefficients 𝐴𝑖𝑗 and

𝐺𝑖𝑗, which contribute to determine 𝐻𝑖𝑖,𝑡 by the following formulation:

𝐻𝑖𝑖,𝑡 = 𝐶𝑖𝑖2 + 𝐴𝑖𝑖

2 𝜖𝑖,𝑡−12 + 2𝐴𝑖𝑖𝐴𝑖𝑗𝜖𝑖,𝑡−1𝜖𝑗,𝑡−1 + 𝐴𝑖𝑗

2 𝜖𝑗,𝑡−12 +

𝐺𝑖𝑖2𝐻𝑖𝑖,𝑡−1 + 𝐺𝑖𝑖𝐺𝑖𝑗𝐻𝑖𝑗,𝑡−1 + 𝐺𝑖𝑗

2 𝐻𝑗𝑗,𝑡−1. (17)

In the last step of our analysis we assume that some shocks, denoted by 𝐬𝑡, perturb

the matrix 𝐻𝑡. Therefore, 𝐬𝑡 is an unpredictable vector of shocks occurring at time

𝑡 and affecting the future realizations of 𝐻𝑡. The VIRF methodology consists of

evaluating the conditional expectation of 𝐻𝑡 with and without the shock 𝐬𝑡.


99

In order to identify the VIRF, the 𝑣𝑒𝑐ℎ representation of the model in Eq. (15) is

used:

𝑣𝑒𝑐ℎ(𝐻𝑡) = 𝑣𝑒𝑐ℎ(𝐶) + 𝑅 ⋅ 𝑣𝑒𝑐ℎ(𝛜𝑡𝛜𝑡′ ) + 𝐹 ⋅ 𝑣𝑒𝑐ℎ(𝐻𝑡−1), (18)

where 𝑣𝑒𝑐ℎ(⋅) is the operator stacking the lower fraction of an 𝑁 × 𝑁 matrix into

an 𝑁∗ = 𝑁(𝑁 + 1)/2 dimensional vector, and 𝑅 and 𝐹 are the matrices with

(𝑁∗)2 elements. 𝐸[𝑣𝑒𝑐ℎ(𝐻𝑡|𝐼𝑡−1)] represents the baseline scenario, where no

shocks are happened. The ℎ-step-ahead VIR is given by:

𝑉ℎ(𝐳𝑡) = 𝐸[𝑣𝑒𝑐ℎ(𝐻𝑡+ℎ|𝐬𝑡, 𝐼𝑡−1)] − 𝐸[𝑣𝑒𝑐ℎ(𝐻𝑡+ℎ|𝐼𝑡−1)]. (19)

In Eq. (19), the VIRF is obtained comparing the ℎ-step-ahead expected conditional

covariance matrix, once the shock at time 𝑡 is occurred, to the baseline scenario.

In this work, we only assume that the shock concerns the series 𝑗. Following the

𝑣𝑒𝑐ℎ representation used in Eq. (18), the one-step-ahead VIRF is:

𝑉1(𝐬𝑡) = 𝑅 ⋅ {𝑣𝑒𝑐ℎ(𝐻𝑡1/2

𝐬𝑡𝐬𝑡′ 𝐻𝑡

1/2) − 𝑣𝑒𝑐ℎ(𝐻𝑡)}, (20)

where 𝐬𝑡 is:

𝐬𝑡 = 𝐻𝑡−1/2

𝛜𝑡, (21)

and 𝐻𝑡−1/2

coming out from the Jordan decomposition of the conditional

covariance matrix:

𝐻𝑡1/2

= Γ𝑡Λ𝑡1/2

Γ𝑡′, (22)

where Λ𝑡 is a diagonal matrix containing the eigenvalues of 𝐻𝑡 , and Γ𝑡 is a

2 × 2 matrix of the corresponding eigenvectors.

Finally, for ℎ ≥ 2, the VIR becomes:

𝑉ℎ(𝐬𝑡) = (𝑅 + 𝐹) ⋅ 𝑉ℎ−1(𝐬𝑡). (23)

3. Empirical analysis

Daily data on African stock markets and the considered commodities were collected

from the Eikon Thomson Reuters provider. The sample period slightly changes

across the series, depending on the availability of the prices, spanning at a minimum

from August 2004 to January 2019 (Uganda), while at its longest it goes from

September 1999 to January 2019. The quotations synthesized in the African stock

market indexes are expressed in their local currency, whereas all the commodities

are in United States dollars ($). The chosen index for the Egyptian stock market is

100 Amendola et al.

EGX 30, which is a weighed index of the top 30 most highly capitalized and liquid

stocks listed on that exchange. As regards the Nigerian stock market, we consider

the NGSE all share index, which reports the movements of all the listed equities.

FTSE/JSE all share index is the chosen capitalization-weighted index of the South

Africa Stock Exchange, whose constituents include up to the top 99% of all the

listed equities in that exchange. With reference to the Tunisian market index, we

opt for TUNINDEX, which is a capitalization-weighted index. Uganda Stock

Exchange and Lusaka Stock Exchange all share indexes are the chosen market

indexes for Uganda and Zambia, respectively made up of 17 and 24 listed

companies. Oil, Gas, Gold and Copper commodities considered here are futures

contracts exchanged in the New York Mercantile Exchange.

As mentioned earlier, the criterion to choose the commodities was their weight as

export shares in these emerging countries, according to the most recent statistics

provided by World Integrated Trade Solution database of the World Bank. For

instance, in 2017 Nigeria exported over $ 36 billion in Oil while the global amount

of its exports was about $ 44.5 billion.

Tables 1 and 2 synthesize some summary statistics related to the daily returns for

African stock markets and commodities, respectively. All series are not symmetric

and have a high skewness and kurtosis.

Table 1: Emerging African stock market daily log–returns statistics

Country Index Time-span Obs. Mean Stand.

Dev.

Skewness Kurtosis 𝒂 Top Comm.

Export 𝑏

Egypt EGX 30 1999-09-01 / 2019-01-28 4731 0.061 1.694 -0.353 8.438 Petroleum,

Gold

Nigeria NGSE 1999-09-01 / 2019-01-28 4812 0.038 0.986 0.096 3.296 Petroleum,

Natural Gas

South Africa FTSE/JSE 1999-09-01 / 2019-01-28 4855 0.043 1.192 -0.172 3.539 Coal, Gold

Tunisia TUNINDEX 1999-09-01 / 2019-01-28 4795 0.042 0.520 -0.071 7.499 Petroleum

Uganda USE 2004-08-03 / 2019-01-15 2682 0.056 1.484 0.109 6.017 Coffee, Gold

Zambia LUSE 1999-09-01 / 2019-01-28 4707 0.067 1.066 0.308 8.702 Copper Percentage scale.

𝑎 The reported value is the excess kurtosis.

𝑏 The column shows the top two commodities, if available, exported by the country according to the World Integrated Trade

Solution database.

Table 2: Energy and metal commodities daily log–returns Commodity Index Time-span Obs. Mean Stand.

Dev.

Skewness Kurtosis 𝒂

Oil CLc1 1999-09-01 / 2019-01-28 4870 0.018 2.382 -0.133 3.928

Gas NGc1 2000-01-04 / 2019-01-28 4788 0.006 3.409 0.485 5.617

Gold GCc1 1999-09-01 / 2019-01-28 4870 0.034 1.070 -0.128 2.431

Copper HGc1 1999-09-01 / 2019-01-28 4878 0.025 1.721 -0.174 4.346 Percentage scale.

𝑎 The reported value is the excess kurtosis.


101

The patterns of the four commodity prices are shown in Figure 1. The most notable

feature in the Oil commodity is the surge of the period 2007-2008, culminated in a

sharp decrease. The other energy commodity, Gas, has a similar pattern with respect

to that of Oil. This is in line with the assumption that both the series are

interconnected, largely documented in literature (see, for instance, Hartley et al.,

2008 and Villar and Joutz, 2006, among others). As regards the behavior of the

metal commodities analyzed here, Gold price seems to have an increasing trend

from the beginning of the sample period up to 2011, while Copper, even if with less

variations, has more than one discernible dynamic pattern. Consistent with these

dynamics is the work of Rossen (2015), where the author claims that the co-

movements are not properly a feature of metal commodities. For the sake of

completeness, in Figure 2 we report the time series of the stock market indices

which we have considered.

Figure 1(a): Oil

Figure 1(b): Gas

Figure 1(c): Gold

Figure 1(d): Copper

Figure 1: Commodity prices

102 Amendola et al.

Figure 2(a): Egypt

Figure 2(b): Nigeria

Figure 2(c): South Africa

Figure 2(d): Tunisia

Figure 2(e): Uganda

Figure 2(f): Zambia

Figure 2: African stock market prices

Step 1

Our first step consists of applying the volatility spillover test between series 𝑗 and

series 𝑖. As mentioned above, the volatility of the commodity series 𝑗 has been

estimated by means of the DAGM model, with a Student’s t-distribution for the

innovation term. The connections between the economic factors and commodity

volatilities has been recently investigated by Prokopczuk et al., 2019. The

description of the MVs used in this work, all taken in the first differences,


103

influencing each single series 𝑗 is provided in Table 3. All the MVs have been

obtained from the Federal Reserve Economic Data [FRED] site. Notably, Table 3

reports also a Granger Causality test for different (monthly) lagged period of the

MV influencing the (monthly) aggregated volatility of series 𝑗. The null of absence

of Granger Causality has been almost always largely rejected.

Table 3: Macroeconomic variables influencing commodities

Macroec. variable Index

Commodity

influenced Granger Test 𝒂 Source

Industrial Production:

Crude oil

IPG211111CS

Oil

l=1, 2.10 Mo et al. (2018)

Karali and Ramirez (2014)

Karali and Power (2013)

l=6, 5.30***

l=12, 3.16***

Industrial Production:

Natural gas

IPG2212S

Gas

l=1, 3.27* Karali and Ramirez (2014)

Karali and Power (2013) l=6, 1.56

l=12, 1.59*

Gross Domestic

Product (GDP):

Normalized for the

United States

USALORSGPNO

STSAM

Gold

l=1, 7.47***

Mo et al. (2018)

Bapna et al. (2012) l=6, 3.82***

l=12, 2.53***

Industrial Production

INDPRO

Copper

l=1, 0.41 Mo et al. (2018)

Slade and Thille (2006) l=6, 4.77***

l=12, 4.22*** 𝑎 The column reports the F-statistics of the Granger Causality test, aiming at verifying if the variables in the first column

Granger causes the volatility of the variables in the third column, with three different lags 𝑙. Being the macroeconomic

variable observed monthly, the monthly aggregated volatility is considered. The tests cover the period January 2001 -

December 2018. ∗, ∗∗ and ∗∗∗ denote significance at the 10%, 5% and 1% levels, respectively.

The DAGM estimates with some residuals diagnostics are reported in Table 4.

Looking at the DAGM estimates, the intuition that positive and negative MVs

variations may have different impact on the volatility of the commodity variable is

confirmed: in some cases, only positive MV variations have an effect, in some

others the opposite occurs. One of the main contribution of this work, the estimation

of the DAGM with a Student’s t-distribution, leads to a plausible and statistically

significant set of degrees of freedom for all the commodities returns. More

importantly, the performances of the DAGM models are always statistically

superior than that of the standard GARCH-MIDAS [GM] model, according to the

Diebold and Mariano (1995) test. In order to fairly compare the two models, also

the GM has been estimated with a Student’s t-distribution. The DAGM models have

also a better fit than the GM model, in terms of the Akaike Information Criterion

[AIC]. Also the residual diagnostics are generally good, as shown in the last six

rows of Table 3. In particular, the p-values of the Ljung-Box and Lagrange

Multiplier (Engle, 1982) tests for conditional heteroskedasticity are reported, with

respect to different lags. Independently of the lag considered, the squared

104 Amendola et al.

standardized residuals appear homoskedastic.

Table 4: DAGM estimates of commodity volatilities

Oil Gas Gold Copper

𝛼 0.019*** 0.073*** 0.036 0.025***

(0.007) (0.013) (0.029) (0.009)

𝛽 0.948*** 0.92*** 0.97*** 0.966***

(0.009) (0.01) (0.044) (0.013)

𝛾 0.05*** -0.022 -0.012 0.014

(0.011) (0.016) (0.019) (0.017)

𝜙 -7.459*** -6.261*** -63.321 -12.864***

(0.312) (0.244) (182.997) (0.679)

𝜃+ -0.325** -0.06 2.439*** -0.183

(0.15) (0.039) (0.214) (0.65)

𝜔2+ 1.68*** 2.541*** 1.813*** 2.248

(0.331) (0.681) (0.131) (119.086)

𝜃− -0.068 0.187*** 2.713 0.36**

(0.223) (0.063) (182.091) (0.148)

𝜔2− 1.484 2.081*** 15.78*** 21.992***

(5.859) (0.181) (0.001) (0.081)

𝑑𝑓 9.428*** 6.69*** 6.55*** 6.407***

(0.744) (1.001) (1.517) (2.134)

DM -6.7*** -5.348*** -4.569*** -2.044**

AIC-DAGM -27990.976 -24079.069 -29118.895 -25142.896

AIC-GM -27512.802 -23801.056 -28723.911 -25140.895

LB 5 0.505 0.892 0.019 0.029

LB 10 0.435 0.719 0.151 0.169

LB 20 0.562 0.865 0.448 0.495

LM 5 0.51 0.879 0.018 0.036

LM 10 0.431 0.702 0.153 0.197

LM 20 0.497 0.855 0.428 0.516 Notes: Standard errors are in parentheses. The additional volatility determinants are shown in Table

3. 𝑑𝑓 is the Student’s t degrees of freedom. ∗, ∗∗ and ∗∗∗ denote significance at the 10%, 5%

and 1% levels, respectively. DM stands for the Diebold-Mariano two-tailed test statistics, whose

null is of equal predictive forecasting ability between the DAGM and the competing model, the

GARCH-MIDAS [GM]. If the test statistic is negative, it means that the DAGM outperforms the

competing model. LB 𝑙 represents the p-values of the Ljung-Box test at 𝑙 lag, applied on squared

standardized residuals. LM 𝑙 represents the p-values of the Lagrange Multiplier (Engle, 1982) test

for conditional heteroskedasticity with 𝑙 lags, always applied on the squared standardized residuals.

The p–values of the LR test concerning the presence of volatility spillovers are

reported in Table 4. As a result, Oil transfers impact and inertial spillovers to Egypt,

Nigeria, Tunisia and Zambia (that is, Oil → Egypt, Oil → Nigeria, Oil →


105

Tunisia and Oil → Zambia). Moreover, we find that Gas → Zambia, Gold →

Uganda and Gold → Zambia, and finally, Copper influences the stock markets of

Tunisia, Uganda and Zambia. South Africa is the only county considered that does

not receive spillovers from any of the considered commodities, according to Def. 1.

Table 5: P-values of the volatility spillover test

Country Lag Oil Gas Gold Copper

Egypt

𝑡 − 1 0.001 0.990 0.052 0.000

𝑡 − 2 0.005 1.000 0.037 0.141

𝑡 − 3 0.001 0.997 0.048 0.767

Nigeria

𝑡 − 1 0.004 0.637 0.961 0.827

𝑡 − 2 0.000 0.428 0.358 0.763

𝑡 − 3 0.006 0.644 0.379 0.904

South Africa

𝑡 − 1 0.097 1.000 0.812 0.453

𝑡 − 2 0.399 0.834 0.673 0.673

𝑡 − 3 0.567 1.000 0.057 0.567

Tunisia

𝑡 − 1 0.000 0.691 0.359 0.000

𝑡 − 2 0.000 0.558 0.215 0.000

𝑡 − 3 0.000 0.447 0.257 0.470

Uganda

𝑡 − 1 0.273 0.441 0.000 0.153

𝑡 − 2 0.250 0.469 0.000 0.000

𝑡 − 3 0.544 0.430 0.014 0.000

Zambia

𝑡 − 1 0.000 0.000 0.000 0.000

𝑡 − 2 0.000 0.000 0.000 0.000

𝑡 − 3 0.000 0.000 0.000 0.000 Notes: The table presents the p-values of the LR test to detect the impact and inertial spillover

originating from commodity 𝑗 (Oil, Gas, Gold or Copper) and transferring to country 𝑖 (first

column), for different lagged periods (second column). Dark, medium-dark, and light shades of gray

denote significance at the 1%, 5%, and 10% levels, respectively.

Step 2

Having established which commodity originated a impact and inertial spillover

towards a African country, we focus on the size and persistence of such a spillover

by using the VIRF. The VIRF requires an estimate of the conditional covariance

matrix, obtained in this step by means of the BEKK model, whose estimates for the

ten relationships highlighted before are reported in Table 5. Some interesting points

emerge. First, there is some evidence of bidirectional, impact and inertial spillovers:

this happens for the relationships Oil and Tunisia and Zambia, Copper and Tunisia,

Uganda and Zambia, because of the jointly significance of the coefficients 𝐴𝑖𝑗, 𝐴𝑗𝑖,

𝐺𝑖𝑗 and 𝐺𝑗𝑖. However, we only explore the issues with the direction 𝑗 → 𝑖, for the

reasons explained above, while we assume that these bi-directional relationships

may be due to some spurious interdependencies. Second, some impact spillovers

are found: from Oil to Tunisia and Zambia, from Copper to Tunisia, Uganda and

Zambia, because of the significance of the 𝐴𝑖𝑗 parameters. A third aspect to

106 Amendola et al.

underline is the presence of inertial spillovers from Oil to Tunisia and Zambia, from

Copper to Tunisia, Uganda and Zambia and finally from Gold to Zambia. This

derives from the high significance of the coefficient 𝐺𝑖𝑗 for the previous

relationships. In summary, the BEKK analysis allows to disentangle the impact and

inertial spillovers of the commodity 𝑗 towards country 𝑖.

Table 6: BEKK estimates 𝒋

(source)

Oil Oil Oil Copper Gold Copper Oil Gas Gold Copper

𝒊

(recipient)

Egypt Nigeria Tunisia Tunisia Uganda Uganda Zambia Zambia Zambia Zambia

𝐶𝑖𝑖

0.454*** 0.376*** 0.188*** 0.263*** 0.099*** 0.326*** 0.780*** 0.052*** 0.176*** 0.468***

(0.041) (0.023) (0.010) (0.013) (0.026) (0.011) (0.024) (0.008) (0.012) (0.018)

𝐶𝑗𝑖

0.000 0.000 0.000 -0.001 0.010*** 0.006*** 0.000* 0.001 0.009*** 0.001***

(0.001) (0.000) (0.000) (0.001) (0.001) (0.001) (0.000) (0.002) (0.000) (0.000)

𝐶𝑗𝑗

-0.005*** 0.004*** 0.003** 0.000 0.003 0.000 0.003*** 0.008*** -0.001 0.000

(0.001) (0.000) (0.001) (0.000) (0.002) (0.001) (0.000) (0.001) (0.001) (0.000)

𝐴𝑖𝑖

0.390*** -0.562*** -0.480*** -0.537*** 0.280*** 0.274*** 0.502*** -0.218*** 0.232*** -0.387***

(0.023) (0.025) (0.021) (0.012) (0.021) (0.006) (0.023) (0.011) (0.002) (0.016)

𝐴𝑗𝑖

7.379*** -1.126 1.077*** -3.302*** -22.697*** 16.116*** -2.043** 1.757*** -4.977*** -6.076***

(1.459) (0.705) (0.298) (0.436) (2.420) (1.362) (0.998) (0.312) (0.981) (1.078)

𝐴𝑖𝑗

0.000 -0.001* 0.001*** -0.002*** 0.000 -0.001** 0.001*** 0.000 0.000 -0.003***

(0.000) (0.000) (0.001) (0.001) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000)

𝐴𝑗𝑗

0.312*** 0.288*** 0.284*** 0.281*** 0.217*** 0.269*** 0.301*** -0.357*** -0.314*** 0.278***

(0.013) (0.011) (0.009) (0.013) (0.039) (0.014) (0.011) (0.014) (0.025) (0.016)

𝐺𝑖𝑖

0.872*** 0.742*** 0.808*** -0.664*** 0.947*** -0.857*** -0.506*** 0.974*** 0.955*** 0.791***

(0.017) (0.026) (0.017) (0.025) (0.007) (0.011) (0.032) (0.003) (0.001) (0.013)

𝐺𝑗𝑖

3.982 0.125 -0.829*** -3.191*** 4.514*** 26.973*** -0.748 -1.183 -13.348*** 5.090***

(3.957) (0.369) (0.073) (0.373) (1.097) (2.473) (0.830) (1.007) (0.536) (0.498)

𝐺𝑖𝑗

0.000 0.000 0.002*** 0.003*** 0.000 0.005*** 0.001*** -0.001 -0.002*** -0.003***

(0.001) (0.000) (0.000) (0.001) (0.000) (0.000) (0.000) (0.001) (0.000) (0.000)

𝐺𝑗𝑗

0.927*** 0.942*** 0.946*** -0.955*** 0.006 0.773*** -0.945*** -0.910*** -0.349*** 0.942***

(0.007) (0.005) (0.009) (0.003) (0.019) (0.023) (0.005) (0.008) (0.056) (0.005)

Notes: Standard errors are in parentheses. *, (**), and (***) denote significance at the 10%, 5%, and 1% levels, respectively.


107

Step 3

The last step of our analysis consists of investigating the response of volatility to a

given shock in the series of the commodity. This step employs the VIRF

methodology and is focused only on the relationships underlined in Table 4 in which

both the impact and the inertial spillovers are significant. As described above, this

happens for the relationships Oil → Tunisia, Copper → Tunisia, Copper →

Uganda, Oil → Zambia and Copper → Zambia. For each of the previous

relationships, we report the volatility impulse responses for three situations. The

first situation consists of a calm period, where the commodity log-returns is close

to its mean. The second and the third situations occur when the commodity log-

return exhibits its minimum and maximum value. We call these situations 𝑡𝑐, 𝑡𝑛,

and 𝑡𝑝 , where the suffixes 𝑐 , 𝑝 , and 𝑛 stand for “calm”, “negative”, and

“positive” periods. We report all the results relatively to the estimated conditional

volatility at the date of the shock. Thus, all the following results are expressed in

percentage.

Oil → Tunisia

The consequences of Oil shocks to Tunisia stock market are illustrated in Figure 3.

A negative shock (Figure 3(a)) has a larger persistence (more than 60 days) and a

larger impact (more than 0.4% bigger volatility) than what happens in case of

positive shock. As expected, relatively to these two circumstances, the effect of no

shock on the Tunisia stock markets is negligible.

Figure 3(a): 𝒕𝒏 = 2001-09-24

Figure 3(b): 𝒕𝒄 = 1999-10-20

Figure 3(c): 𝒕𝒑 = 2008-12-22

Figure 3: Volatility Impulse Response from Oil to Tunisia

Copper → Tunisia

Three main points can be highlighted in Figure 4. First, after both a Copper price

increase and decrease, the volatility of Tunisia’s stock market increases. Second, a

positive shock in the Copper market lets higher the Tunisia’s stock market volatility

(up to 0.8% larger) than a negative shock (up to 0.3% larger). Third, the stock

market volatility of Tunisia increases and sharply decreases (the effect cancels after

10 days) if the Copper price is invariant.

108 Amendola et al.

Figure 4(a): 𝒕𝒏 = 2008-10-10 Figure 4(b): 𝒕𝒄 = 1999-11-17 Figure 4(c): 𝒕𝒑 = 2008-10-29

Figure 4: Volatility Impulse Response from Copper to Tunisia

Copper → Uganda

Figure 5 illustrates the volatility responses of Uganda’s stock market after a given

shock in Copper prices. The greatest impact takes place when a negative shock

occurs in Copper prices. In this case, the volatility is expected to increase up to 1.5%

(the day after the shock). Instead, calm and positive periods let the stock market

volatility invariant.


Figure 5: Volatility Impulse Response from Copper to Uganda

Oil → Zambia

In Figure 6 the VIRs of Oil on the Zambia’s stock market are illustrated. In the left

plot, describing the results on the stock market volatility of a negative shock in Oil

prices, the volatility increases up to 0.4%, while the effect cancels after 30 days,

approximately. Not surprisingly, the effects of a calm and positive periods in the

Oil prices are much less evident.


109


Figure 6: Volatility Impulse Response from Oil to Zambia

Copper → Zambia

As highlighted in Table 1, Copper is the main exported good by Zambia. This

maybe justify the size of a negative shock in the Copper prices and affecting the

Zambia’s stock market. In this case, the stock market volatility of Zambia increases

up to 2%, with a persistence of over 50 days, while the effects after the other two

types of shocks appear negligible, as highlighted in Figure 7.


Figure 7: Volatility Impulse Response from Copper to Zambia

4. Conclusion

In this paper we have addressed a rarely investigated issue, that is, the dependence

of the most important African stock markets (Egypt, Nigeria, South Africa, Tunisia,

Uganda and Zambia) upon the price fluctuations of energy and metal commodity

markets (Oil, Gas, Gold and Copper). The idea is that for countries in which

commodity exports are a relevant share of their trade, economic activity as reflected

in the variations in quoted stock prices will depend on what commodity price

volatility is. The reverse is not arguable given the tiny importance of these markets

in the global allocation of resources. The paper is hence empirically motivated in

its effort to ascertain which bilateral links are relevant in defining channels of

transmission.

110 Amendola et al.

We build a methodology to address this research question. Our approach moves

within the GARCH framework and has a pre-testing phase where an extended

GARCH specification of a stock market conditional variance includes the

possibility of additional explanatory power coming from the most recent lagged

squared (log-)returns (what we call impact) and conditional variance (what we call

inertia) from a single commodity. Given the complex interactions at work in global

portfolio allocations and in demand/supply of a commodity, chances are that even

commodities that are not directly among the natural resources exported by a country

may affect stock markets. To be noted as a relevant original contribution is the

adoption of the DAGM model for the commodity volatility which gives us the

opportunity to introduce some information about macroeconomic variables

observed at world level driving a low-frequency component of volatility reacting to

different phases of the business cycle. Another methodological innovation of this

paper is the estimation of the DAGM model in a Student’s t framework, in order to

take into account the leptokurtosis of the commodity (log-)returns.

The first step has highlighted ten significant relationships originating from the four

energy and metal commodities and affecting the African Stock markets: Oil affects

the stock markets of Egypt, Nigeria, Tunisia and Zambia, Gold those of Uganda and

Zambia, Copper those of Tunisia, Uganda and Zambia and finally Gas affects the

stock market of Zambia. Therefore, two points can be underlined. First, the stock

market of Zambia is the most vulnerable market to commodity price variations

among the considered emerging countries. Second, countries with the largest share

of exports given by a commodity have a stock market whose volatility is also

influenced by that commodity. This happens for:

(i) the stock markets of Egypt, Nigeria and Tunisia, which mainly export

Oil and whose stock markets depend on the impact and the inertia of this

commodity.

(ii) (ii) the stock market of Uganda, whose volatility depends also on the

variations of Gold prices, which is one of the main exporting good of

that country.

(iii) (iii) the stock market of Zambia, whose exports are mainly based on

Copper, is in turn influenced by Copper impact and inertia.

In the next phase, a bivariate BEKK–MGARCH model for a pair of commodity and

relevant market isolated under the first step has estimated. By means of this set of

BEKK models, the commodity impact and inertial spillovers towards the country

stock market’s volatility have taken into account. And, only the significant

relationships are considered in order to address the last step of our analysis,

consisting of the analysis of the VIRF. These relationships are: Oil – Tunisia,

Copper – Tunisia, Copper – Uganda, Oil – Zambia and Copper – Zambia. The VIRF

defines the profile of the convergence of the conditional volatility to the

unconditional level, following an impulse - in this case a shock applied to the

commodity to trace its trajectory into the volatility of the national stock market: we

have presented different profiles according to a characterization of starting

conditions in the market which may change according to whether the market goes


111

through a phase of tranquillity or turbulence. We have seen the most interesting

profiles as those Volatility Impulse Responses where non monotonicity and slower

convergence to the long run equilibrium level were detected. In particular,

turbulence periods occurring today in the commodity prices tend to increase the

tomorrow stock market volatility.

A word is in order about the fact that focusing the attention on emerging markets is

often frustrated by reduced data availability and/or data quality. This is truly

unfortunate because economic development is also the result of how institutions

work and the desire for quantitative research to offer some policy options. In this

respect, the unavailability of the intra-daily quartet Open–High–Low–Close for

these major African stock markets keeps us away from being able to apply a

volatility spillover analysis in the vein of Engle et al. (2012) on a direct measure of

volatility such as the daily range.

112 Amendola et al.

References

[1] Adjasi, C.K. and Yartey, C.A. (2007). Stock market development in Sub-

Saharan Africa: critical issues and challenges. International Monetary Fund

(IMF) Working Paper 209.

[2] Amendola, A., Candila, V. and Gallo, G.M. (2019). On the asymmetric impact

of macro–variables on volatility. Economic Modelling, 76, pp. 135 - 152.

[3] Amendola, A., Candila, V. and Scognamillo, A. (2017). On the influence of

US monetary policy on crude oil price volatility. Empirical Economics, 52, 1,

pp. 155 - 178.

[4] Asgharian, H., Christiansen, C. and Hou, A.J. (2015). Macro-finance

determinants of the long-run stock–bond correlation: The DCC-MIDAS

specification. Journal of Financial Econometrics, 14, pp. 617 - 642.

[5] Bapna, I., Sood, V., Totala, N.K. and Saluja, H.S. (2012). Dynamics of

macroeconomic variables affecting price innovation in gold: a relationship

analysis. Pacific Business Review International, 5, 1, pp. 1 - 10.

[6] Bauwens, L., Laurent, S. and Rombouts, J.V.K. (2006). Multivariate GARCH

models: a survey. Journal of Applied Econometrics, 21, pp. 79 - 109.

[7] Berg, K.A. and Vu, N.T. (2019). International spillovers of US financial

volatility. Journal of International Money and Finance, 97, 19 - 34.

[8] Bollerslev, T. (1986). Generalized autoregressive conditional

heteroskedasticity. Journal of Econometrics, 31, pp. 307 - 327.

[9] Bollerslev, T. (1987). A conditionally heteroskedastic time series model for

speculative prices and rates of return. Review of Economics and Statistics, 69,

3, pp. 542 - 547.

[10] Borensztein, E. and Reinhart, C.M. (1994). The macroeconomic determinants

of commodity prices. IMF Staff Papers 41, 2, pp. 236 - 261.

[11] Candila, V. and Farace S. (2018). On the volatility spillover between

agricultural commodities and Latin American stock markets. Risks, 6, 4, pp. 1

- 16.

[12] Chang, C.L. and McAleer, M. (2017). A simple test for causality in volatility.

Econometrics, 5, 1, pp. 1 - 5.

[13] Chevallier, J. and Ielpo, F. (2013). Cross-market linkages between

commodities, stocks and bonds. Applied Economics Letters, 20, 10, pp. 1008

- 1018.

[14] Conrad, C., Loch, K. and Rittler, D. (2014). On the macroeconomic

determinants of long-term volatilities and correlations in U.S. stock and crude

oil markets. Journal of Empirical Finance, 29, pp. 26 - 40.

[15] Conrad, C. and Loch, K. (2015). Anticipating long-term stock market volatility.

Journal of Applied Econometrics, 30, 7, pp. 1090 - 1114.

[16] Diebold, F.X. and Mariano, R.S. (1995). Comparing predictive accuracy.

Journal of Business & Economic Statistics, 13, 3, pp. 253 - 263.


113

[17] Diebold, F.X. and Yilmaz, K. (2008). Macroeconomic volatility and stock

market volatility, worldwide. Working Paper 14269, National Bureau of

Economic Research.

[18] Diebold, F.X. and Yilmaz, K. (2009). Measuring financial asset return and

volatility spillovers, with application to global equity markets. The Economic

Journal, 119, 534, pp. 158 - 171.

[19] Diebold, F.X. and Yilmaz, K. (2012). Better to give than to receive: Predictive

directional measurement of volatility spillovers. International Journal of

Forecasting, 28, 1, pp. 57 - 66.

[20] Economic Commission for Africa et al. (2018), African Statistical Yearbook

2018.

[21] Engle, R.F., Gallo, G.M. and Velucchi, M. (2012). Volatility spillovers in East

Asian financial markets: a MEM–based approach. Review of Economics and

Statistics, 94, 1, pp. 222 - 223.

[22] Engle, R.F. and Gallo, G.M. (2006). A multiple indicators model for volatility

using intra-daily data. Journal of Econometrics, 131, pp. 3 - 27.

[23] Engle, R.F., Ghysels, E. and Sohn, B. (2013). Stock market volatility and

macroeconomic fundamentals. Review of Economics and Statistics, 95, 3, pp.

776 - 797.

[24] Engle, R.F. (1982). Autoregressive conditional heteroscedasticity with

estimates of the variance of United Kingdom inflation. Econometrica, 50, pp.

987 - 1007.

[25] Engle, R.F. (2002). New frontiers for ARCH models. Journal of Applied

Econometrics, 17, pp. 425 - 446.

[26] Engle, R.F., Ito, T. and Lin, W.L. (1990). Meteor showers or heat waves?

Heteroskedastic intra daily volatility in the foreign exchange market.

Econometrica, 58, pp. 1749 - 1778.

[27] Engle, R.F. and Kroner, F.K. (1995). Multivariate simultaneous generalized

ARCH. Econometric Theory, 11, pp. 122 - 150.

[28] Granger, C.W.J. (1969). Investigating causal relations by econometric models

and cross-spectral methods. Econometrica, 37, 3, pp. 424 - 438.

[29] Greenwood-Nimmo, M., Nguyen, V.H. and Rafferty, B. (2016). Risk and

return spillovers among the G10 currencies. Journal of Financial Markets, 31,

pp. 43 - 62.

[30] Hafner, C.M. and Herwartz, H. (2006). Volatility impulse responses for

multivariate GARCH models: An exchange rate illustration. Journal of

International Money and Finance, 25, 5, pp. 719 - 740.

[31] Hamao, Y., Masulis, R.W. and Ng, V. (1990). Correlations in price changes

and volatility across international stock markets. The Review of Financial

Studies, 3, 2, pp. 281 - 307.

[32] Hartley, P.R., Medlock III, K.B. and Rosthal, J.E. (2008). The relationship of

natural gas to oil prices. The Energy Journal, 29, 3, pp. 47 - 65.

114 Amendola et al.

[33] Hou, Y.G. and Li, S. (2020). Volatility and skewness spillover between stock

index and stock index futures markets during a crash period: New evidence

from China. International Review of Economics & Finance, 66, pp. 166 - 188.

[34] Ildırar, M. and Iscan, E. (2016). The interaction between stock prices and

commodity prices: Eastern Europe and Central Asia case. International Journal

of Economics and Finance Studies, 8, 2, pp. 94 - 106.

[35] Kang, S.H., Ko, H.-U. and Yoon, S.-M. (2017). Contagion effects and

volatility impulse responses between US and Asian stock markets. Korea and

the World Economy, 18, 2, pp. 111 - 130.

[36] Kang, W., Ratti, R.A. and Yoon, K.H. (2015). The impact of oil price shocks

on the stock market return and volatility relationship. Journal of International

Financial Markets, Institutions and Money, 34, pp. 41 - 54.

[37] Karali, B. and Power, G.B. (2013). Short- and Long-Run Determinants of

Commodity Price Volatility. American Journal of Agricultural Economics, 95,

3, pp. 724 - 738.

[38] Karali, B. and Ramirez, O.A. (2014). Macro determinants of volatility and

volatility spillover in energy markets. Energy Economics, 46, 413 - 421.

[39] Karanasos, M., Ali, F.M., Margaronis, Z. and Nath, R. (2018). Modelling time

varying volatility spillovers and conditional correlations across commodity

metal futures. International Review of Financial Analysis, 57, pp. 246 - 256.

[40] Kim, B.-H., Kim, H. and Lee, B.-S. (2015). Spillover effects of the US

financial crisis on financial markets in emerging Asian countries. International

Review of Economics & Finance, 39, pp. 192 - 210.

[41] Korkmaz, T., Çevik, E.İ. and Atukeren E. (2012). Return and volatility

spillovers among CIVETS stock markets. Emerging Markets Review, 13, 2,

pp. 230 - 252.

[42] Lin, W.-L., Engle, R.F. and Ito, T. (1994). Do bulls and bears move across

borders? International transmission of stock returns and volatility. Review of

Financial Studies, 7, 3, pp. 507 - 538.

[43] Mo, D., Gupta, R., Li, B. and Singh T. (2018). The macroeconomic

determinants of commodity futures volatility: Evidence from Chinese and

Indian markets. Economic Modelling, 70, pp. 543 - 560.

[44] Nazlioglu, S., Cumhur, E. and Soytas U. (2013). Volatility spillover between

oil and agricultural commodity markets. Energy Economics, 36, pp. 658 - 665.

[45] Neaime, S. (2012). The global financial crisis, financial linkages and

correlations in returns and volatilities in emerging MENA stock markets.

Emerging Markets Review, 13, 3, pp. 268 - 282.

[46] Prokopczuk, M, Stancu, A. and Symeonidis, L. (2019). The economic drivers

of commodity market volatility. Journal of International Money and Finance,

98, pp. 1 - 13.

[47] Rossen, A. (2015). What are metal prices like? Co-movement, price cycles and

long-run trends. Resources Policy, 45, pp. 255 - 276.


115

[48] Silvennoinen, A. and Thorp, S. (2013). Financialization, crisis and commodity

correlation dynamics. Journal of International Financial Markets, Institutions

and Money, 24, pp. 42 - 65.

[49] Slade, M.E. and Thille, H. (2006). Commodity spot prices: An exploratory

assessment of market structure and forward-trading effects. Economica, 73,

290, pp. 229 - 256.

[50] Sugimoto, K., Matsuki, T. and Yoshida, Y. (2014). The global financial crisis:

An analysis of the spillover effects on African stock markets. Emerging

Markets Review, 21, pp. 201 - 233.

[51] Villar, J.A. and Joutz, F.L. (2006). The relationship between crude oil and

natural gas prices. Energy Information Administration, Office of Oil and Gas,

pp. 1 - 43.

Energy and non energy Commodities: Spillover Effects on ...

Documents

Transcript of Energy and non energy Commodities: Spillover Effects on ...